Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

Quantum-Chemical Study of the Profiles of Reactions that Form Pyrrole Anion N-Adducts with CS<Subscript>2</Subscript> and CO<Subscript>2</Subscript>

The profiles of reactions leading to pyrrole anion N-adducts with CO₂ and CS₂ have been studied by the ab initio (RHF/6-31+G*, MP2/6-31+G*) and density functional (B3LYP/6-31+G*) methods. Addition of the pyrrole anion to the carbon disulfide molecule is accompanied by the appearance of a minimum corresponding to a pre-reaction complex. The transformation of the complex to the N-pyrrolyldithiocarboxylate anion occurs via a low activation barrier, which is due to repolarization of the C=S bonds. The profile of the reaction leading to the pyrrole anion N-adduct with CO₂ does not contain any intermediate stationary points throughout the whole route from reagents to products.Original Russian Text Copyright © 2004 by V. B. Kobychev, N. M. Vitkovskaya, I. L. Zaitseva, and B. A. Trofimov__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 990–993, November–December, 2004.     

Novel route to synthesis of allyl starch and biodegradable hydrogel by copolymerizing allyl‐modified starch with methacrylic acid and acrylamide

Maize starch was modified by allyl chloride adopting an interfacial reaction technique with cetyltrimethyl ammonium bromide as a phase‐transfer catalyst and pyridine as an acid acceptor. The degree of substitution was determined from an increasing carbon content of the modified starch. The percentage of carbon and hydrogen of the allyl‐modified starch was estimated by elemental analysis (C, H, and N), and the product characterization was done through ¹H NMR and ¹³C NMR analyses. The allyl‐modified starch was then copolymerized with methacrylic acid and a combination of methacrylic acid and acrylamide at 50 and 70 °C with potassium persulfate as an initiator. The copolymer thus formed swelled in distilled water after neutralization with sodium carbonate. The percentage of absorption capacity of the hydrogels was determined with distilled water and 0.9% NaCl solution. The highest percentage of absorption, 6500%, was achieved for the developed hydrogel containing allyl starch and acrylic monomer in a 1.7:1 w/w ratio and acrylic monomer, namely, methacrylic acid and acrylamide in a 3.2:1 w/w ratio. The study on biodegradability of the developed hydrogel showed that the hydrogel is degradable in the presence of diastase (amylase). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1650–1658, 2003     

The LEM exponential integrator for advection–diffusion–reaction equations

We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.     

Synthesis of poly-yne polymers containing transition metals,disilane, disiloxane and phosphine groups in the main chain

The synthesis and characterization of metal poly-yne polymers containing disilane, disiloxane and phosphine groups in the main chain are described. The platinum and palladium poly-yne polymers were synthesized by polycondensation reactions between a metal chloride and an α, ω-bisethynyl complex in amines in the presence of cuprous iodide as a catalyst. The nickel poly-yne polymers were synthesized by an alkynyl ligand exchange reaction between a nickel acetylide and an α, ω-bisethynyl complex in diethylamine in the presence of cuprous iodide as a catalyst. The reaction of the platinum poly-yne polymer, containing disiloxane groups in the main chain, with copper (I) salts afforded adducts of η-²-bonded σ-acetylide polymer complexes. The reactions of the palladium poly-yne polymer, containing phosphine groups in the main chain, with transition-metal carbonyl complexes afforded polymer complexes which have phosphorus in the main chain-transition-metal bonds. A concentrated solution of the platinum poly-yne polymer containing disiloxane groups in the main chain forms a lyotropic liquid crystal in dichloromethane or 1, 2-dichloroethane.     

Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

t—BuNO二聚体在不同溶剂中裂解机理的研究

本文利用＾１ＨＮＭＲ，ＵＶ－Ｖｉｓ方法，研究了ｔ－ＢｕＮＯ二聚体在有机溶剂及水溶液中的裂解反应产物，分析了其反应的动力学，提出了在非极性的有机相中ｔ－ＢｕＮＯ二聚体为均裂反应，而在极性的水相中为均裂和异裂同时进行的竞争反应。     

Mechanism of the thermal decomposition of nitrates from graphite furnace mass spectrometry studies

A basically new mechanism of the thermal decomposition of solids is proposed to explain the mass spectral observations of gaseous molecules of CoO, CuO, Cu₂O, NiO, PbO and Mg(OH)₂ during the low-temperature decomposition of the anhydrous and hydrated nitrates of these metals. The mechanism consists of two stages: congruent gasification of all reaction products irrespective of their saturated vapor pressure and subsequent condensation of the low-volatility species (oxides and hydroxides). The partial pressures of these species at the appearance temperatures calculated from this theory for the first stage of the process (1–50 mPa) are in agreement with the detection limits of the quadrupole mass spectrometers used in these experiments. The proposed mechanism is supported by other available data obtained by thermal analysis.     

在局部区域上的奇摄动反应扩散方程初始边值问题

本文是讨论一类在局部区域上的奇摄动反应扩散初始边值问题.利用算子理论和 不动点原理,得到了相应问题解的存在性和唯一性.